Introduction: Big Draws

First we have to define what constitutes a big draw. While there is no one standard definition, for the purposes of this discussion we will define a big draw as one that has more than 9 outs to improve against Top Pair. It's not a perfect definition as a) sometimes we aren't up against Top Pair but rather a stronger hand against which we have fewer outs b) sometimes (but infrequently) we improve to the second best hand. But overall I feel this is a good starting definition to distinguish these draws from smaller, garden-variety 8- and 9- out draws like OESD and small Flush Draws.

Examples of Big Draws:

1. Nut Flush Draw: A9 on a J72 flop. This draw has 12 outs to improve against all Top Pair and Overpair hands other than AJ and AA. Against JT-/QJ/KJ/QQ/KK we have 12 outs, and so based on our definition above the NFD just barely makes it as a Big Draw.

2. Pair + OESD: 88 on 679. This draw has 10 outs against a hand like A9.

3. Pair + Flush Draw: A9 on a J92 flop. This draw has 14 outs (9 diamonds, 2 9s and 3 As) against KJ and 11 outs against AJ.

4. Flush Draw + Gutshot: A9 on a J87. This draw has 12 out (9 diamonds and 3 non-diamond Ts vs. a hand like AJ.

5. Flush Draw + Overs: AK on a T72 flop. This draw has anywhere between 15 outs against a hand like JT or JJ to 12 outs against a hand like AT.

6. Flush Draw + OESD or OESFD: 89 on a T72 flop or a A:J on a T98 flop.

Key Concepts:

1. Tension between Implied Odds and Fold Equity. Usually there is an inverse relationship between Implied Odds (IO) and Fold Equity (FE). The higher the Fold Equity the lower the Implied Odds and vice versa.

2. Straight draws are harder for opponents to see and therefore have higher Implied Odds. Flush draws are easier for opponents to see and therefore have lower implied odds.

3. All else equal, you should lean towards calling rather than raising with draws most of whose outs have high implied odds.

4. Semi-bluffing requires fold equity. If your knowledge of your opponents makes you strongly believe that they will not fold any of their original range in a given situation, then semi-bluffing makes no sense.

5. Bluffing Outs. When there are multiple draws possible on a board and you have the draw with a high Implied Odds component (e.g. Pair + OESD) you can sometimes call with the plan on value betting when one of your hard-to-see outs comes in AND also bluffing when the 'obvious' draw such as a flush draw but which you do not have comes in.

6. Position enhances the value of draws, both when bluffing and when extracting value.

7. High stack depth/High SPR increase the fold equity of big draws vs. medium-strength hands.

8. Always keep track of the strength of villain's Original Range (O-range) and their Continuing Range (C-range). The further they continue, the stronger their C-range becomes, which means Implied Odds go up and Fold Equity goes down. For example, if you raise a big draw in position after a tight opponent c-bets the flop, and he calls and then bets the turn, it is very unlikely that opponent is folding much of his range on the turn with normal stack depth, but it is quite possible that he will call off the rest of his stack on the river even when an obvious draw comes in.

9. Big draws shrink when facing strong multi-way action, as it becomes increasingly likely that one of the opponents is holding a better draw and another a better made hands (see the last example below). This is a good time to re-evaluate and let an otherwise 'big' draw go.

Sample Equities

Pair + FD vs. a TP+ range

A9 on a J92 flop. If we think we are up against a range of TPGK+, our equity is:

Board: Jd 9s 2d
Dead:

equity win tie pots won pots tied
Hand 0: 45.036% 45.03% 00.00% 20508 1.50 { Ad9d }
Hand 1: 54.964% 54.96% 00.00% 25029 1.50 { JJ, 99, 22, AJs, KJs, QJs, J9s, AJo, KJo, QJo, J9o }

Same situation but if the range we are up against strengthens to TPTK+, our equity drops to 39%. If it's 2pr+ our equity drops to 35%.

Flush Draw + OESD: A:J on a T98 flop. Our equity against a range that's Overpairs+ is:

Board: Td 9d 8s
Dead:

equity win tie pots won pots tied
Hand 0: 49.090% 47.51% 01.58% 34336 1141.50 { AdJd }
Hand 1: 50.910% 49.33% 01.58% 35651 1141.50 { 88+, QJs, T9s, 98s, 76s, QJo, T9o, 98o, 76o }

Against 2pr+ our equity drops slightly to 47%.


Hand Examples

1. NFD In Position

(note: I am doing this one the long-hand. I don't claim to have all the answers but wanted to put in some solid work on different lines. If you are in the 'tl;dr' camp - do us both a favor and 'dr' silently).

Villain is a solid TAG. He understands which boards are good for c-betting and capable of folding marginal hands under pressure, although he is not weak-tight and does not require the nuts to continue against raises. Effective stacks are 100bbs.

Villain opens to 4bbs in EP. We call OTB with AQ.

At this point we believe that villain's range is something like:

{AA-22,AKo-AJo,AKs-ATs,KQs-KJs,QJs,JTs,T9s,98s,87s,76s}

We think that 77+, AQ+ part of the range is always there, and 22-66, SCs and weaker suited Broadway is there some portion of the time depending on opponent specifics, how tough/weak he perceives the game, etc. Our pre-flop equity against that range is only ~ 38% but we believe that we can take away the pot on certain flops using position.

Flop (8.5bbs): K72

Villain c-bets for 6bbs. At this point we can't narrow villain's range much as this is the board we believe based on his tendencies he will c-bet near 100% of the time. Here is how his pre-flop range, which we also believe to be his flop c-betting range, distributes on this flop:

Two-Pair+ 6%
Top Pair: 12%
2nd Pair/Middle Pair: 25%
3rd Pair: 17%
Flush Draw: 5%
Air: 35%
(source: Flopzilla)

Using Poker Stove our equity against his c-betting range is: 59%. Folding is out of the question, and it's a question of whether we call or raise.

Option A: Calling Flop

One question we should always ask is who is more likely to make a mistake on this and future streets as a result of our action. We should also think about how our hand's equity changes on a blank turn.

Here, if we call, villain is unlikely to double-barrel turn with the air part of his range. If our draw comes in, it will be obvious to our opponent, so he will not commit his whole stack with the vast majority of his range. He might bet/fold the turn if the flush comes in for a little over half pot with TP+ and c/f with the rest of his range.

Scenario 1: Turn completes our draw (3).

Our equity changes to almost 100%.

So his turn continuing range is: {KJs, KQs, AKs, KK+, 22-33, 77, 9d8d-JdTd}. That's 32% of the original range that c-bet the flop. Of this range, we can assume that 60% (TP and Overpair) is bet/folding and 40% (sets and flushes) is bet/calling. Our villain is making a mistake when he is betting any part of his range on this turn against our specific hand. I do not believe that he is making a mistake against our overall flop-calling range in this situation. If our places were reversed we would probably play the turn similarly.

The above assumptions lead us to believe that when he checks the turn his range is too weak to call any reasonable bet, and he is checking to c/f rather than c/c.

Scenario 2: Turn is a blank (3)

Our equity against his original range drops slightly from 58% to ~ 53%

Let's assume he bets the same range as in scenario 1 or {KJs, KQs, AKs, KK+, 22-33, 77, 9d8d-JdTd}. Our equity against his turn betting range drops to ~ 27%. He is unlikely to make a mistake with any part of his range if we call as he is unlikely to call off his stack if we call turn and a flush comes in on the river. An interesting question is whether or not we can credibly take the call flop/shove blank turn line. If he folds all the TP- part of his betting range, then we can get him to make a mistake with that part of his range. Furthermore, I am not 100% sure, but I feel some players have a sizing tell here on the turn - if they intend to bet/fold turn they bet smaller, closer to 50% of pot than if they intend to bet/call.

If he checks, his range is as weak as in Scenario 1 but now he is much more likely to c/c the 2nd pair/middle pair part of his range so I don't think we can make him make a major mistake by floating flop and betting a blank turn when checked to.

Option B: Raising Flop

Instead of flatting villain's 6bb c-bet on the flop, we can raise it to say 24bbs. I think it's safe to assume that a solid TAG opponent is definitely going to fold everything except: {KJs, KQs, AKs, AA, 22, 77, KK, 9d8d-JdTd}. That means that he is folding ~ 70% of his c-betting range. We are risking 24bb to win 14.5bb and need a fold ~62% of the time if our EV is 0 if villain doesn't fold, so this means our flop raise is +EV just based on our Fold Equity.

If villain 3 bet-shoves, we can assign a range of {KK, 22, 77 and 9d8d-JdTd}. Our equity against that range is 33%. We have to call 66bb, so the EV of our call is near zero. In practice, since sets are always in the range but FDs are in the range less than 100% of the time we should probably fold.

The interesting case happens when Villain just calls. This range is the toughest to assign. Some TAGs will fold hands like KJs and KQs on the flop. Others will call with all TPs and AA and some 2nd pairs. Let's say that this TAG is not willing to fold TP on the flop here and that his flop calling range is: {AA, KJs, KQs, AK}. Our equity against that range on a blank turn is only 22%. So the question is, with the pot being 57bbs and us having 72bbs behind, do we have fold equity against his flop calling range if he checks? I think this depends on a lot of gameflow variables. In a vacuum, I honestly don't know and would err on checking behind turn at 2/5 NL and below but am open to others' thoughts.

2. Pair + FD In Position

Villain is the same TAG from Example 1 above. He opens in EP with the same range of: {AA-22,AKo-AJo,AKs-ATs,KQs-KJs,QJs,JTs,T9s,98s,87s,76s}

We flat OTB with 67.

Flop (8.5bbs): K72

Villain c-bets for 6bb. If we assume that he is c-betting his entire range as we did in Example 1, our equity is higher than before, or ~ 66%. On a blank turn, our equity against his original range drops, but not that much, to ~60%.

If we say the blank turn is a 3, and we assume his turn betting range is: {KK+,77,33-22,KJs+,AdQd,AdJd,AdTd,QdJd,JdTd,Td9d,9d8d}, our equity on the turn against that range is 35%. That means that we can profitably call a less than pot-sized bet. However, we have to play the river carefully to make sure we avoid RIO if he open-shoves/pots a diamond river. In that case we might have to fold. However, if the diamond comes in, we can profitably bet 1/2 pot and expect to get looked up by a number of worse hands like sets and AA and possibly AK.

On the other hand, if we raise flop, our fold equity is similar to that in example 1 (~65%), but our equity against the range that 3-bet shoves the flop is 40% if he always shoves all draws and 36% if he only includes the NFDs in his flop 3-betting range. So with stacks set-up where he c-bets for 6bbs, we raise to 24bbs and he shoves, we are getting the odds to call.

Of the two lines, I personally like flatting better when in position, because I think there are more ways for our opponent to make a mistake on future streets than if we raise, but I think both lines are +EV.

Note: The above two examples were against a decent TAG capable of folding medium-strength hands to some pressure. Against someone who is more stationy than that, it becomes more correct to flat since our implied odds go up and fold equity goes down. Since most 2/5NL and below opponents are known for calling too much, you should seriously consider opponent tendencies and how much fold equity you really have before semi-bluffing in position. I am still tempted to semi-bluff big draws that have mostly obvious outs OOP, given the difficulty of extracting value on turn/river when we hit against all but the most stationy opponents.

Finally, here is an example of when we want to release a big draw:

3. Pair + FD facing multi-way action.

NIT opens in EP for 4bbs. We call OTB with 67 and a solid TAG flats in the BB. Stacks are 100bb.

Flop (12bb): KT7

BB leads for pot, EP NIT raises to 40bbs and its our action. Here is our equity:


Board: Kd Td 7s
Dead:

equity win tie pots won pots tied
Hand 0: 40.499% 40.29% 00.21% 84050 428.00 { TT, 77, AdQd, AdJd, Ad9d, Ad8d, Ad6d, Ad5d, Ad4d, Ad3d, Ad2d }
Hand 1: 17.827% 17.83% 00.00% 37186 0.00 { 7d6d }
Hand 2: 41.674% 41.47% 00.21% 86501 428.00 { KK+, TT, AKs, AKo }


Even though we might think we have a 'big draw', between BB's range having a lot of draws that dominate us if we do improve and the EP NIT's range being almost all made hands that, our equity against both of them combined is terrible and we have no fold equity. We should fold.


Conclusion

I tried to do my best to go over both the concepts I view as key, and give some examples with a more in-depth than usual analysis. I know this was somewhat long, and even though it's long it's by no means complete. I welcome all additions/corrections/further thoughts, as I did this part to give back to the forum and in part to force myself to do in-depth Poker Stove/Flopzilla range analysis to inform my own play at the table.

I'm glad to see a COTM from you. This is very well-written and thought out. I want to point out that key concept #9 is the most abstract and, personally, the concept that came least naturally to me.

Anyone can calculate equity based on outs in a HU hand. Figuring out outs based on the action in a multiway hand is a much tougher problem that takes really good guesswork.

Another good example similar to situation 3 would involve showing how awful your equity drops is when chasing a NFD + SD in a 4 way pot in which everyone shows interest. Often, one person has the made hand and the other 3 are eating up each other's outs and have almost no shot to win.

I am digesting this as I read through it. It's a concept I need to really work on when it comes to live play. So, for that, thank you. However, I would have liked to see our villain be a more typical player at these stakes. TAGs are rare in my experience. And, a 4x raise isn't too reasonable for my games, either. I would have liked to also see 6x raise sizes or multiple callers with the 4x size since that's what it usually brings along.

NH. I agree that the joy of the semi-bluff is much diminished when against LP opponents. OTOH, something to consider is that raising your draw can also improve your implied odds, because the larger pot can get more later action from loose/passive opponents, esp the ones who would never put you on a draw, because you were betting.

This obviously only applies to the drooliest games, IMO. Even casino 1/2 often thinks well enough to avoid that trap.

An example is that you're facing heat with 54 on a board:

K63.

If one of the villains is on Ax and another holds 66, you are almost drawing dead in these spots.

I used a decent TAG as a 'border case'. This is a player capable of folding medium hands when facing pressure but not a weak-tight player who is going to give up with everything but the near-nuts. From there, you can adjust based on your specific opponents' tendencies.

Against weak-tight players fold equity goes up against their range, so a semi-bluffing line becomes better, but once they continue their continuing range is much stronger than a TAG's, so fold equity drops off and implied odds increase.

Against a player much more call-y than in my example, the opposite happens. Fold equity is lower, and implied odds go up. Ever hear a guy say something like 'Did that third diamond make your flush? Just my luck, can't believe it came on the river. Darn, I have top pair, I have to call'? That's the kind of guy who you want to take more passive lines against since you will get paid a decent amount of the time when you hit on some of you more obvious outs.

My overall goal wasn't to come up with cookie-cutter lines for your guys to use, but to outline some concepts and go through examples of the thinking process that you should use in your games, taking into account your opponent tendencies and other factors of your games. The process doesn't change, but which line to take might depending on your specific situation.

To add to Concept #3 in the OP. I was playing with one of the better 5/10 regs @ Foxwoods and saw him call twice with KQ in position on a JT23r board. I asked him after the hand (I wasn't involved) why he didn't raise the flop. He replied that he strongly felt that the bettor either hand a hand like AJ which would improve to a 2nd-best hand if he made Broadway or would use the river A as a barrel card. So even though he clearly wasn't getting the explicit odds on the turn with enough money behind and position his call x 2 was > flop raise since it maximized the chances for his opponent to make a costly mistake on an expensive street.

Setsy,

Would you say that tighter the villain is in these spots, the lower the frequency that hero should raise?

Nice op, hopefully we can all get a bettor understanding of a "monster draw" in this forum.

I think 'tightness' is only one thing to think about. I am assuming by 'tighter' you mean his pre-flop tendencies. So tighter pre-flop means his range is stronger when he c-bets the flop. That means less fold equity. However, we also need to understand villain's post-flop tendencies. Is he fit/fold post-flop? Is he too sticky with strong one-pair hands (common for people who are tight pre-flop)? But overall yes, the stronger someone's range is the less we should be semi-bluffing and the more we should be calling for implied odds, all else equal.

Thanks for that little clarification, Setsy. As I said, I was digesting and was not all the way through when I posted because I was nodding off, literally. Upon reading it through with a clearer mind, I saw where you were going and thought you were quite thorough. It's going to be a helpful post for a former online player converting to live.

This might be the concept least-discussed in the OP. Setsy, can you elaborate here?

My understanding is that when a mid-strength hand has a lot of chips behind, it has trouble continuing vs. your raise because of its own larger reverse implied odds.

[And this is why we might raise certains hands that are likely to turn into high top pair type hands big enough pf that we can profitably c-bet shove, if we have stack sizes that are difficult to work with on multiple streets.]

I am a little hesitant as this is very opponent specific, and this being LLNL I don't want to say something that might be mis-applied vs. stations who never fold any decent piece.

That being said, it goes back to the concept of SPR. HU, it's usually correct to commit with TPGK in the 0-4 range against most opponents. Nobody can really exploit you if you do this, as even if sometimes they flop a set and stack you, they weren't getting the right odds. Against some it's correct to commit with SPRs as high as 7-8. With over pairs the range shifts a little higher, to say 0-7 against most and as high as 10 against some.

Now think of it from the point of view of the one with a big draw wanting fold equity. If you are facing an opponent with an SPR of less than 4, he is going to be committed with a much bigger range than if you face that same opponent with an SPR of 13+. So in the second case your fold equity is higher, making semibluffs more profitable.

So as a practical example, lets say you raise OTB with AKs to 3bb with 100bb stacks. A TAG 3-bets you from the BB to 12bb and you elect to flat rather than 4-bet. Your SPR will be 88/24 or around 3.5. Say you flop NFD+Overs. Your fold equity against over pairs is going to be lower here than in a higher SPR pot as he is very likely not folding his over pairs. Which means you have good implied odds btw.... So if he c-bets 14bb into 24bb, flatting might be better than raising.

Same opponent but now he opens from MP for 4bb and you flat with AQs OTB and see a flop HU. Now your SPR is 96/9 or around 11. If you flop a big draw, your opponent is much more likely to fold a one pair hand than he would be in the first example. Or change the first example to 300bb stacks, and again your fold equity goes way up.

The other concept when semibluffing to keep in mind is the idea of leverage. Basically the idea is that you are risking only a portion of the effective stack in order to put your opponent to a decision for his whole stack since you know whether you will follow through on a later street for the rest but he doesn't, and if he calls your bet on that street he is frequently deciding right there whether to commit his whole stack or not. This becomes more important as stacks get deeper as it's more important to figure out the right line to be the one to put n the last leveraged bet in.

But with all this talk of semibluffing, remember that most of you aren't playing against good opponents deep at your stakes. The logical conclusion IMO is you should semibluff your draws less and flat more (in position). Semibluffing becomes a much better tool once people can let go of TP hands. I have played in some 5/10 games which play deep and tight where people are just waiting to cooler each other. So there the correct adjustment becomes to bluff/semi-bluff more since people are waiting for the near-nuts to commit. In games most of us play daily the correct adjustment is the opposite.

This whole statement helps me as much as your OP got me thinking. All I can do while thinking through examples is say to myself, "But, they don't freaking fold TP or draws (draws I know I want calling me). How effective is pumping a big draw really going to be?" I hate this aspect of my games because as a former online TAG-lite, I really have to holster my hands when I catch a combo draw at these live tables. And, it kills me to continually have to do this. But, it always appears correct to play a bit more passively ip and still rarely c/r oop because I don't know my villains well enough to think they can fold if they actually show interest in the pot by betting.

So, I guess the conclusion I am coming back to is: I'm really only playing draws fast when I have a pot-equity edge on the flop. But, there have to be some other situations where it's best to pump the draw....I just can't seem to find one yet and am afraid I'm being too nitty.